On the Near Impossibility of Measuring the Returns to Advertising by Randall A Lewis, Justin M. Rao :: SSRN

Evidence from the randomized trials is very weak because individual-level sales are incredibly volatile relative to the per capita cost of a campaign — a “small” impact on a noisy dependent variable can generate positive returns. A calibrated statistical argument shows that the required sample size for an experiment to generate informative confidence intervals is typically in excess of ten million person-weeks.